Recursion in language: a new approach

1. A procedure is recursive if part of it involves running the entire procedure anew. The output of such a procedure is also called recursive. For example, the procedure that draws the famous Droste can picture in (1) at some point involves calling the very same procedure, in order to draw that can in the picture. (1) However, one cannot tell that an object is recursive by simply looking at it: one has to know by what procedure it was derived. For example, the picture in (1) could have been generated in a nonrecursive way (and it probably was), for instance by assigning a color to each pixel. In another example, consider the situation in (2), from the comic strip ‘Calvin and Hobbes’, where the boy Calvin finds himself surrounded by five duplicates of himself. (2) As Calvin exclaims, the procedure bringing this situation about was recursive: Calvin made a duplicate of himself, and the duplicate proceeded to make a duplicate of himself, etc. However, Calvin could have created five duplicates by simply repeating the duplication process five times, yielding an iterative rather than a recursive procedure. In language, it is commonly taken for granted that structures involving some kind of embedding are recursive. Typical examples are in (3): (3) a. John thinks that Mary said that it was raining b. the height of the letters on the cover of reports from the government The structures in (3) are recursive if they are generated by a recursive procedure, such as the rewrite rules of preminimalist generative grammar. The procedure generating (3a) may be paraphrased as in (4), showing recursion in that to interpret ‘clause ’ in (4b), one must run (4a) again. (4) a. clause = subject + predicate b. predicate = verb + clause Similarly with the procedure in (5) generating (3b): (5) a. determiner phrase = determiner + noun phrase b. noun phrase = noun + preposition phrase c. preposition phrase = preposition + determiner phrase For this reason, embedding is taken to signal recursion, underlying much of the debat